Question: Below is the graph of $y = a \csc bx$ for some positive constants $a$ and $b.$  Find $a.$

[asy]import TrigMacros;

size(500);

real g(real x)
{
	return 2*csc(x/3);
}

draw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red);
draw(graph(g,-3*pi + 0.01,-0.01),red);
draw(graph(g,0.01,3*pi - 0.01),red);
draw(graph(g,3*pi + 0.01,6*pi - 0.01),red);
limits((-6*pi,-5),(6*pi,5),Crop);
draw((-3*pi,-5)--(-3*pi,5),dashed);
draw((3*pi,-5)--(3*pi,5),dashed);
trig_axes(-6*pi,6*pi,-5,5,pi/2,1);
layer();
rm_trig_labels(-11, 11, 2);

label("$1$", (0,1), E);
label("$2$", (0,2), E);
label("$3$", (0,3), E);
label("$4$", (0,4), E);
label("$-1$", (0,-1), E);
label("$-2$", (0,-2), E);
label("$-3$", (0,-3), E);
label("$-4$", (0,-4), E);
[/asy]
Answer: For the part where the function is positive, the minimum value is 2.  The minimum value of $y = a \csc bx,$ where $y$ is positive, is $a.$  Therefore, $a = \boxed{2}.$